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Topological Field Theory with Haagerup Symmetry

Huang, Tzu-Chen and Lin, Ying-Hsuan (2021) Topological Field Theory with Haagerup Symmetry. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210219-122651478

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Abstract

We construct a (1+1)d topological field theory (TFT) whose topological defect lines (TDLs) realize the transparent Haagerup H₃ fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data -- three-point functions and lasso diagrams -- are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. Many of the constraints we derive are not limited to the this particular TFT with six vacua, and we leave open the question of whether the Haagerup H₃ fusion category is realized in TFTs with two or four vacua. Finally, TFTs realizing the Haagerup H₁ and H₂ fusion categories can be obtained by gauging algebra objects. This note makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2102.05664arXivDiscussion Paper
ORCID:
AuthorORCID
Huang, Tzu-Chen0000-0002-8738-7695
Lin, Ying-Hsuan0000-0001-8904-1287
Additional Information:We thank Yuji Tachikawa for suggesting this interesting project, for helpful advice, and for comments on the first draft. We also thank Chi-Ming Chang, Shu-Heng Shao, and Yifan Wang for enlightening discussions. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. YL is supported by the Simons Collaboration Grant on the NonPerturbative Bootstrap and by the Sherman Fairchild Foundation.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2021-006
Record Number:CaltechAUTHORS:20210219-122651478
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210219-122651478
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108128
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:19 Feb 2021 20:36
Last Modified:19 Feb 2021 20:36

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